## Spectral Resolution and Slit Width

Below is a conservative estimate of the trend of resolution or
FWHM (full-width at half-maximum) versus slit width for the
instrument using a TEK CCD.
The spatial scale is **~0.69 arcsecs/pixel.**
It should be pointed out that there is a general trend of slightly
poorer focus as one goes from the center of the field to the edge.
In the spatial direction, the trend is about a 20%
degradation when going from center-to-edge along a spectral line (at field
center).

Diagram of Resolution vs. Slit Width

## Slit Width Selection

The usual procedure for slit width selection has been to match
the resolution of the detector by dividing the actual slit width by
the so-called demagnification factor, or the ratio of collimator-to-camera
focal lengths. However, for spectrographs such as the RC spectrograph,
this approximation is not always valid. For cases when the
collimator-to-camera angle is greater than ~15 degrees, the full
expression for projected slit width should be used.

w = r (fcam / fcoll) W

Here *w* is the projected slit width, *W* the actual
(physical) slit width,
and *r* is the "grating anamorphic magnification". The factor *r*
is a function of the grating tilt and collimator-camera angle, i.e.

r = cos(t + phi/2) / cos(t - phi/2)

where *phi* is the collimator-camera angle (46 degrees)
and *t* is the grating tilt.
For the UV Fast Camera, the camera-to-collimator focal ratio is ~0.23 .
At large grating inclinations the anamorphic
demagnification factor becomes significant. In these cases the slit can be
opened slightly wider without degrading the resolution.
See F. Schweizer's article
**PASP** *91*, No. 539, 149, 1979 for more information.
For a complete table of grating tilts for the RC Spectrograph see the FTP
version of the manual.

Be aware that at high grating inclinations (tilt <=3500) the camera
becomes over-filled resulting in throughput loss.
This is a problem only with higher dispersion gratings.

Plot of Anamorphic Factor

*deveny@noao.edu*

Friday, August 4, 1995